Third Hankel Determinant for Ma-Minda Bi-univalent Functions
Received:September 05, 2018  Revised:October 26, 2018
Key Word: analytic function   Hankel determinant   Ma-Minda bi-univalent function   upper bound
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11561001; 11271045), the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (Grant No.NJYT-18-A14), the Natural Science Foundation of Inner Mongolia (Grant No.2018MS01026), the Higher School Foundation of Inner Mongolia (Grant Nos.NJZY17300; NJZY17301) and the Natural Science Foundation of Chifeng of Inner Mongolia.
 Author Name Affiliation Haiyan ZHANG School of Mathematics and Computer Science, Chifeng University, Inner Mongolia 024000, P. R. China Huo TANG School of Mathematics and Computer Science, Chifeng University, Inner Mongolia 024000, P. R. China
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In this paper, we investigate the third Hankel determinant $H_{3}(1)$ for the class $H^{\mu}_{\sigma}(\lambda, \varphi)~(\lambda\geq1,~\mu\geq1)$ of Ma-Minda bi-univalent functions in the open unit disk $\mathbb{D}=\{z:|z|<1\}$ and obtain the upper bound of the above determinant $H_{3}(1)$.